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Abstract:

Apparatus and methods related to memory resistors are provided. A
feedback controller applies adjustment signals to a memristor. A
non-volatile electrical resistance of the memristor is sensed by the
feedback controller during the adjustment. The memristor is adjusted to
particular values lying between first and second limiting values with
minimal overshoot. Increased memristor service life, faster operation,
lower power consumption, and higher operational integrity are achieved by
the present teachings.

Claims:

1. An apparatus, comprising: a memristor characterized by a non-volatile
electrical resistance; and a feedback controller configured to adjust the
non-volatile electrical resistance to one or more particular values
between a first limiting value and a second limiting value, the feedback
controller electrically coupled to the memristor in a closed-loop control
arrangement at least during the adjustment of the non-volatile electrical
resistance.

2. The apparatus according to claim 1, the memristor configured such that
first limiting value is lesser than the second limiting value.

3. The apparatus according to claim 1, the feedback controller further
configured to adjust the non-volatile electrical resistance of the
memristor by way of electrical pulses.

4. The apparatus according to claim 3, the feedback controller further
configured to control at least the frequency of the electrical pulses,
the amplitude of the electrical pulses, or e polarity of the electrical
pulses.

5. The apparatus according to claim 1, the feedback controller further
configured to adjust the non-volatile electrical resistance of the
memristor by way of a direct-current bias voltage.

6. The apparatus according to claim 1, the feedback controller further
configured to adjust the non-volatile electrical resistance of the
memristor by way of proportional-integral-derivative control.

7. The apparatus according to claim 1, the feedback controller including
a comparator electrically coupled to a reference voltage, the comparator
also electrically coupled to the memristor at least during the adjustment
of the non-volatile electrical resistance.

8. The apparatus according to claim 1, the memristor being an element of
a Wheatstone Bridge at least during the adjustment of the non-volatile
electrical resistance.

9. The apparatus according to claim 8, the feedback controller including
a comparator electrically coupled across the Wheatstone Bridge at least
during the adjustment of the non-volatile electrical resistance.

10. The apparatus according to claim 1, the feedback controller further
configured to apply a sensing current to the memristor at least during
the adjustment of the non-volatile electrical resistance.

11. A method, comprising: operating an electronic device including a
memristor, the memristor characterized by a non-volatile electrical
resistance of a first value; adjusting the non-volatile electrical
resistance of the memristor from the first value to a second value
different than the first value using a feedback controller; and operating
the electronic device with the memristor characterized by the
non-volatile electrical resistance of the second value.

12. The method according to claim 11, the adjusting the non-volatile
electrical resistance of the memristor performed by way of electrical
pulses controlled by the feedback controller.

13. The method according to claim 11, the adjusting the non-volatile
electrical resistance of the memristor performed by way of
proportional-integral-derivative action of the feedback controller.

14. The method according to claim 11 further comprising monitoring a
balance condition of a Wheatstone Bridge during the adjusting of the
non-volatile electrical resistance of the memristor.

15. The method according to claim 11, the adjusting of the non-volatile
electrical resistance of the memristor performed by way of adjustment
signals, the feedback controller configured to control at least an
amplitude of the adjustment signals, a polarity of the adjustment
signals, or a frequency of the adjustment signals.

Description:

BACKGROUND

[0001] Memory resistors or "memristors" are electronic constructs that
exhibit an adjustable, non-volatile electrical resistance characterized
by a minimum (on, or "low state") and a maximum (off or "high state")
resistance value. Known circuits and applications operate their
memristors at these respective minimum and maximum resistance values,
switching between limiting values as needed. These low and high
resistance states are typically separated by one-thousand to
ten-thousands Ohms.

[0002] However, it has been discovered that memristors may exhibit
undesirably short useful life spans, as well as undesirably high power
consumption. The present teachings address the foregoing concerns.

BRIEF DESCRIPTION OF THE DRAWINGS

[0003] The present embodiments will now be described, by way of example,
with reference to the accompanying drawings, in which:

[0004]FIG. 1 depicts block diagram of an electronic device according to
one embodiment;

[0005]FIG. 2 depicts a flow diagram of a method according to one
embodiment;

[0006]FIG. 3 depicts a schematic diagram of a feedback controller
according to one embodiment;

[0010] Means and methods related to memory resistors (memristors) are
provided. A feedback controller applies adjustment signals to a
memristor. A non-volatile electrical resistance of the memristor is
sensed by the feedback controller during the adjustment. The memristor is
adjusted to particular values lying between first and second limiting
values with minimal overshoot. Increased memristor service life, faster
operation, lower power consumption, and higher operational integrity are
achieved by the present teachings.

[0011] In one embodiment, an apparatus includes a memristor characterized
by a non-volatile electrical resistance. The apparatus also includes a
feedback controller. The feedback controller is configured to adjust the
non-volatile electrical resistance to one or more particular values
between a first limiting value and a second limiting value. The feedback
controller is electrically coupled to the memristor in a closed-loop
control arrangement at least during the adjustment of the non-volatile
electrical resistance.

[0012] In another embodiment, a method includes operating an electronic
device including a memristor. The memristor is characterized by a
non-volatile electrical resistance of a first value. The method also
includes adjusting the non-volatile electrical resistance of the
memristor from the first value to a second value different than the first
value using a feedback controller. The method additionally includes
operating the electronic device with the memristor characterized by the
non-volatile electrical resistance of the second value.

First Illustrative Device

[0013] Reference is now directed to FIG. 1, which depicts a block diagram
of an electronic device 100. The device 100 is illustrative and
non-limiting with respect to the present teachings. Thus, other devices
can be configured, constructed or operated in accordance with the present
teachings. For purposes of non-limiting illustration, it is assumed that
the device 100 represents a memory or logic device. Any number of
different types and embodiments of devices 100 inclusive of the present
teachings are contemplated.

[0014] The device 100 includes a memory resistor, or memristor, 102. The
memristor 102 can be defined by any suitable memristor used during normal
operations of the device 100. For purposes of non-limiting illustration,
it is assumed that the memristor 102 serves a value storage function by
virtue of its ability to be selectively switched (or programmed) between
non-volatile electrical resistance values. For further purposes of
illustration, it is assumed that the memristor 102 is characterized by a
minimum (on, or low state) electrical resistance of one-thousand Ohms and
a maximum (off, or high state) electrical resistance of six-thousand
Ohms.

[0015] The device 100 also includes a feedback controller (controller)
104. The controller 104 can be defined by any such controller
contemplated by the present teachings. The controller 104 is configured
to adjust the non-volatile electrical resistance of the memristor 102 by
application of corresponding electrical signals. The controller 104 is
electrically coupled to the memristor 102, at least during resistance
adjustment (i.e., programming) operations. Appropriate switching (not
shown) can be used to couple and de-couple the memristor 102 from the
feedback controller 104 as needed.

[0016] The electronic device 100 also includes other circuitry 106. The
other circuitry can be defined by or include any electronic circuitry
configured to perform various normal operations of the device 100. Such
other circuitry 106 can thus includes one or more processors, analog
circuitry, digital circuitry, hybrid devices, a state machine, etc. The
other circuitry 106 is electrically coupled to and configured to use the
memristor 102 during normal operations.

[0017] The electronic device 100 further includes other resources 108. The
other resources 108 can be defined by or include any suitable elements or
device used during normal operations of the device 100. Non-limiting
examples of such other resources 108 include a battery or batteries, a
power supply, a user interface, wireless communications circuitry,
network communications circuitry, a microprocessor or microcontroller,
etc. The other resources are coupled to the other circuitry 106 as needed
in order for the device 100 to perform its normal operations.

[0018] The device 100 is depicted as including a single memristor 102 in
the interest of understanding. However, it is to be understood that any
number of memristors 102 can be included within devices contemplated by
the present teachings (e.g., such as a storage array of memristors,
etc.). Additionally, individual addressing, and adjustment of those
numerous memristors by way of feedback control, is contemplated by the
present teachings. It is to be further noted that such memristors
(memristor 102 or others) can be implemented at the integrated circuit
(chip) level, integrated within complementary metal-oxide semiconductor
(CMOS) circuitry. Other embodiments can also be defined and used.

First Illustrative Method

[0019] Attention is now directed to FIG. 2, which depicts a method
according to one embodiment of the present teachings. The method of FIG.
2 depicts particular method steps and an order of execution. However, it
is to be understood that other methods including other steps, omitting
one or more of the depicted steps, or proceeding in other orders of
execution are also contemplated. Thus, the method of FIG. 2 is
illustrative and non-limiting with respect to the present teachings.
Reference is made to FIG. 1 in the interest of understanding the method
of FIG. 2.

[0020] At 200, an electronic device operates normally with a memristor at
a present electrical resistance value. The present resistance value is
also referred to as a first value for purposes of discussion. For
purposes of non-limiting illustration, it is assumed that the electronic
device 100 operates normally with the memristor 102 characterized by a
non-volatile resistance value of two-thousand Ohms.

[0021] At 202, the non-volatile resistance of the memristor is adjusted
using feedback control. For purposes of the ongoing illustration, it is
assumed that the feedback controller 104 applies electrical signaling to
the memristor 102 so as to cause the non-volatile electrical resistance
to be shifted toward another value. The feedback controller 104 monitors
(senses) the instantaneous electrical resistance of the memristor 102
during the adjustment process. The controller 104 stops the adjustment
process just as the memristor 102 reaches the desired resistance. For
non-limiting example, the memristor 102 now exhibits four-thousand Ohms
of non-volatile resistance.

[0022] At 204, the electronic device is operated normally with the
memristor at the new electrical resistance value. For purposes of the
present illustration, it is assumed that the device 100 operates normally
with the memristor 102 at four-thousand Ohms of resistance.

[0023] In general and without limitation, the present teachings
contemplate various devices respectively includes of various number of
memristors. Such devices also include one or more feedback controllers
configured to selectively adjust (or program) the non-volatile electrical
resistance of the memristors on an individually addressable basis.
Feedback signaling is used to monitor the instantaneous resistance value
of a particular memristor during the adjustment process. Multiplexing,
de-multiplexing, switching and other means familiar to one of ordinary
skill in the electronic arts can be used so as access and program
particular memristors during resistance adjustment operations.

[0024] The feedback controller then ceases the applied adjustment stimulus
as the memristor reaches or nears the desired resistance value so as to
minimize or substantially eliminate overshoot. Furthermore, such
adjustments can be made between selected electrical resistance values
that lie well within the minimum-to-maximum range (i.e., low-to-high
states) for the particular memristor. In this way, power consumption is
reduced and memristor longevity is increased relative to programming
techniques that operate strictly between minimum and maximum (i.e.,
"rail-to-rail") resistance values.

First Illustrative Controller

[0025] Reference is now made to FIG. 3, which depicts a schematic diagram
of a feedback controller (controller) 300 according to another embodiment
of the present teachings. The controller 300 is illustrative and
non-limiting in nature. Thus, other controllers are contemplated that
include one or more aspects of the present teachings. The controller 300
is electrically coupled to an illustrative memristor 302 in the interest
of understanding the present teachings. It is to be understood that the
controller 300 can be electrically coupled and de-coupled from the
memristor 302 as needed during resistance adjustment and normal
operations, respectively.

[0026] The controller 300 includes a source of constant direct-current
(DC) electrical energy (source) 304. The source 304 is configured to
drive an electrical current 306 through memristor 302 by way of a
resistor 308. The current 306 is of relatively low value and is selected
to permit sensing the instantaneous resistance value of the memristor
302. In one embodiment, the current 306 is in the range of one-to-ten uA
(microamperes), while the resistor 308 has a value of one-thousand Ohms.
Other suitable respective values of current 306 and resistor 308 can also
be used.

[0027] The controller 300 also includes a comparator 310. The comparator
310 is electrically coupled to a sensing node 312 and to a reference
voltage at a node 314. Voltage present at the node 312 corresponds to the
instantaneous resistance value of the memristor 302. The comparator is
configured to provide an output signal at a node 316 in accordance with a
comparison of the reference voltage at node 314 and the voltage at the
sensing node 312. In this way, the output signal at node 316 corresponds
to the difference (if any) between the instantaneous memristor 302 value
and a desired value established at the reference voltage node 314. The
comparator 310 output signal is also referred to as an error signal. It
is noted that the reference voltage at node 314 can be of selectable
magnitude or polarity (positive or negative) relative to ground node 318.

[0028] The controller 300 also includes a pulse generator 320. The pulse
generator 320 is configured to provide pulses of DC electrical energy of
controllable magnitude and frequency. The pulse generator 320 is coupled
to apply electrical pulses to the memristor 302 by way of a transistor
(i.e., switch) 322 and a coupling capacitor 324. It is noted that the
pulse generator can provide pulses of selective polarity (positive or
negative) relative to ground node 318.

[0029] The controller 300 also includes a transistor 322 as introduced
above. The transistor 322 is coupled to the comparator 310 at output
signal node 316, to the pulse generator 320 and to coupling capacitor
324. The transistor 322 is configured to operate as a switch under the
controlling influence of the comparator 310. That is, electrical pulses
from the pulse generator 320 are routed to the memristor 302 through the
transistor 322 in accordance with the output signaling of the comparator
310.

[0030] It is to be understood that the controller 300 can be defined, in
whole or in part, by selected discrete components. Additionally, the
controller 300 can be defined, in whole or in part, by an
application-specific integrated circuit (ASIC). In yet another
embodiment, the controller 300 can be defined, in whole or in part, by a
microcontroller operating in accordance with a computer-readable program
code. One having ordinary skill in the electrical engineering arts will
appreciate that the controller 300 can be constructed using various
circuit elements, and an exhaustive recitation is not needed for purposes
of understanding the present teachings.

[0031] In one embodiment, the controller 300 includes, or is defined by,
read/write circuitry configured to store values in and retrieve values
from the memristor 302. In such an illustrative and non-limiting
embodiment, the memristor 302 is used as a memory cell or storage
element. Vast memory arrays inclusive of numerous memristors (e.g., 302,
etc.) can be defined and operated using feedback control according to the
present teachings.

[0032] In another embodiment (not shown), a feedback controller is
provided that includes two respective reference voltage nodes, and two
distinct pulse generators. These respective "mirror image" circuit
portions are configured to controllably provide pulses of opposite
polarities to a memristor. That is, one portion causes increases in
memristor resistance value, while the other causes decreases in memristor
resistance value. Such controller circuit portions are coupled to the
memristor by way of suitable multiplexing circuitry.

[0033]FIG. 4 is a signal timing diagram depicting illustrative and
non-limiting operations of the controller 300. As depicted, the memristor
302 is defined by an instantaneous, non-volatile electrical resistance
400 that is adjusted over time. The memristor 302 is further
characterized by a minimum (on, or low state) electrical resistance 402,
and a maximum (off, or high state) electrical resistance 404. The minimum
and maximum electrical resistances 402 and 404 (respectively) are also
referred to as "limiting resistances" for the memristor 302.

[0034] The resistance values 402 and 404 represent lower and upper limits,
respectively, for the electrical resistance achievable by the memristor
302. These values 402 and 404 are also referred to as rail-to-rail
resistances for the memristor 302. For purposes of non-limiting example,
it assumed that the minimum resistance 402 is one-thousand Ohms, and that
the maximum resistance 404 is four-thousand Ohms. The memristor 302
operates with the electrical resistance 400 at a first value 406 during
time period T1. For purposes of non-limiting example, it is assumed that
the first value 406 is two-thousand Ohms.

[0035] Then, during time period T2, a series of electrical pulses (i.e.,
control, or programming signals) 408 are applied to the memristor 302 by
way of controller 300. It is noted that the pulses 408 are characterized
by a particular polarity relative to ground, magnitude and frequency. In
turn, the electrical resistance 400 of the memristor 302 transitions
(increases) during time period T2 from the first value 406 to a second,
greater value 410. For purposes of non-limiting example, it is assumed
that the second value 410 is three-thousand Ohms.

[0036] During the next time period T3, no electrical pulses are applied to
the memristor 302. The memristor 302 maintains the non-volatile
electrical resistance 400 at the second value 410 throughout the time
period T3. Normal operations of other circuitry coupled to (or inclusive
of) the memristor 302 can be performed during time period T3.

[0037] During the next time period T4, a series of electrical pulses 412
is applied to the memristor 302 by way of controller 300. It is noted
that the pulses 412 are characterized by polarity, magnitude and
frequency parameters that are different than those of the pulses 408.
Specifically, the pulses 412 are of opposite polarity, and of greater
frequency and magnitude, relative to the pulses 408.

[0038] In turn, the electrical resistance 400 of the memristor 302
transitions (decreases) during time period T4 from the second value 410
back to the first value 406. It is noted that the magnitude and frequency
of the pulses 412 cause the electrical resistance 400 to shift between
values 410 and 406 in less time during period T4 than during period T2.
That is, the magnitude or frequency (or both) of the electrical pulses
applied by the controller 300 can be respectively controlled so as to
affect the time-rate-of-change of the electrical resistance 400.
Furthermore, the polarity of the electrical pulses determines the
direction of the resistance 400 shift--increasing or decreasing,
respectively.

Second Illustrative Controller

[0039] Reference is now made to FIG. 5, which depicts a schematic diagram
of a feedback controller (controller) 500 according to another embodiment
of the present teachings. The controller 500 is illustrative and
non-limiting in nature. Thus, other controllers are contemplated that
include one or more aspects of the present teachings. The controller 500
is electrically coupled to an illustrative memristor 502 in the interest
of understanding the present teachings. It is to be understood that the
controller 500 can be electrically coupled and de-coupled from the
memristor 502 as needed during resistance adjustment and normal
operations, respectively.

[0040] The controller 500 includes a controllable source of direct-current
(DC) electrical voltage (source) 504. The source 504 is configured to
provide an electrical potential that is controllable by way of the
controller 500 as described hereinafter. As such, the polarity or
magnitude (or both) of the source 504 can be controllably adjusted with
respect to time,

[0041] The controller 500 also includes a plurality of resistors 506, 508
and 510, respectively. The resistors 506-510, inclusive, are of an equal
electrical resistance value "R" Ohms. The resistors 506-510 and the
memristor 502 are electrically coupled to define a Wheatstone Bridge 512.
The Wheatstone Bridge 512 is electrically coupled to the source 504 by
way of a node 514, and to electrical ground potential at a node 516.

[0042] In another embodiment, the memristor 502 is electrically coupled as
an element of the Wheatstone Bridge 512 during resistance adjustment
operations, and is electrically isolated there from at other times. One
of skill in the electrical arts can appreciate that such selective
coupling to the memristor 502 can be performed by way of switches,
relays, transistors or other suitable elements.

[0043] The controller 500 also includes a comparator 518. The comparator
518 is electrically coupled across the Wheatstone Bridge 512. The
comparator 518 is configured to provide an output signal at a node 520 in
accordance with the balance condition of the Wheatstone Bridge 512.
Specifically, when the electrical resistance value of the memristor 502
is equal to that of the other resistors 506-510--that is, "R" Ohms--the
bridge is "balanced" and the comparator 518 senses zero volts
differential across the Wheatstone Bridge 512.

[0044] Conversely, when the memristor 502 resistance value is other than
"R" Ohms, the bridge is "out-of-balance" and the comparator 518 senses a
corresponding (non-zero) electrical voltage across the Wheatstone Bridge
512. The magnitude of the sensed voltage corresponds to the difference
between "R" Ohms and the memristor 502 resistance value. In turn, the
polarity of the sensed voltage corresponds to whether the memristor 502
resistance value is greater than or less than "R".

[0045] In this way, the output signal at node 520 corresponds to the
difference (if any) between the instantaneous memristor 502 value and the
value "R" Ohms as defined by the resistors 506-510. The comparator 518
output signal is also referred to as an error signal. It is noted that
one or more desired (and programmable) memristor 502 resistance values
correspond to respective out-of-balance conditions for the Wheatstone
Bridge 512. Thus, the controller 500 can operate to establish and
maintain such a desired out-of-balance condition during normal
operations.

[0046] The controller 500 further includes a
proportional-integral-derivative (RID) controller 522. The RID controller
522 is configured to receive the comparator 518 output (i.e., error)
signal at node 520 and to provide a control signal output at a node 524.
The signal at node 524 is coupled to the source 504 so as to control the
polarity and time-varying magnitude of the voltage applied to the
Wheatstone Bridge 512. The PID controller 522 is further configured to
control the source 504 in accordance with
proportional-integral-derivative control action. It is important to note
that some particular out-of-balance condition can correspond to a desired
resistance value for the memristor 502, and that such an out-of-balance
condition can define a "setpoint" for the PID controller 522.

[0047] The PID controller 522 can implemented by way of dedicated-purpose
integrated circuitry, a microcontroller operating in accordance with
executable program code, etc. One having ordinary skill in the control
arts is familiar with PID control action, and further elaboration is not
needed for an understanding of the present teachings.

[0048] It is to be understood that the controller 500 can be defined, in
whole or in part, by selected discrete components. Additionally, the
controller 500 can be defined, in whole or in part, by an
application-specific integrated circuit (ASIC). In another embodiment,
the controller 500 can be defined, in whole or in part, by a
microcontroller operating in accordance with a computer readable program
code. One having ordinary skill in the electrical engineering arts will
appreciate that the controller 500 can be constructed using various
circuit elements, and an exhaustive recitation is not needed for purposes
of understanding the present teachings.

[0049] In one embodiment, the controller 500 includes, or is defined by,
read/write circuitry configured to store values in and retrieve values
from the memristor 502. In such an illustrative and non-limiting
embodiment, the memristor 502 is used as a memory cell or storage
element. Memory arrays can be defined and operated using the PID feedback
control contemplated by the present teachings.

[0050] In another embodiment (not shown), a feedback controller is
provided that includes one or more adjustable or selectable resistance
values within a Wheatstone Bridge (e.g., 512). In such an embodiment, the
memristor can be adjusted to some particular resistance value (within the
limiting values) by altering one or more resistor values (i.e., "R1") of
the bridge. The memristor is then reprogrammed under PID control until a
balanced bridge condition is detected.

[0051]FIG. 6 is a signal timing diagram depicting illustrative and
non-limiting operations of the controller 500. As depicted, the memristor
502 is defined by an instantaneous, non-volatile electrical resistance
600 that is adjusted over time. The memristor 502 is further
characterized by a minimum (on, or low state) electrical resistance 602,
and a maximum (off, or high state) electrical resistance 604.

[0052] The resistance values 602 and 604 represent lower and upper limits,
respectively, for the electrical resistance achievable by the memristor
502, and are referred to as limiting values. These values 602 and 604 are
also referred to as rail-to-rail resistances for the memristor 502. For
purposes of non-limiting example, it assumed that the minimum resistance
602 is two-thousand Ohms, and that the maximum resistance 604 is
six-thousand Ohms. The memristor 502 operates with the electrical
resistance 600 of a first value 606 during time period T1. For purposes
of non-limiting example, it is assumed that the first value 606 is
three-thousand Ohms.

[0053] Then, during time period T2, an electrical bias voltage (i.e.,
programming signal) 608 is applied to the Wheatstone Bridge 512 by the
controller 500. This bias voltage 608 is applied so as to affect a change
in the non-volatile electrical resistance of the memristor 502. It is
noted that the bias voltage 608 is characterized by a particular polarity
and a time-varying magnitude in accordance with PID control action. In
turn, the electrical resistance 600 of the memristor 502 transitions
(increases) during time period T2 from the first value 606 to a second,
greater value 610. For purposes of non-limiting example, it is assumed
that the second resistance value 610 is four-thousand Ohms.

[0054] During the next time period T3, no bias voltage is applied to the
Wheatstone Bridge 512. As such, the memristor 502 exhibits the
non-volatile electrical resistance 600 at the second value 610 throughout
the time period T3.

[0055] Thereafter, during time period T4, a bias voltage 612 is applied to
the Wheatstone Bridge 512 by way of controller 500. It is noted that the
bias voltage 612 is characterized by a polarity and time-varying
magnitude that differ from that of the bias voltage 608. Specifically,
the bias voltage 612 is of opposite polarity and of greater peak
magnitude relative to the bias voltage 608.

[0056] In turn, the electrical resistance 600 of the memristor 502
transitions (decreases) during time period T4 from the second value 610
back to the first value 606. It is noted that the time-varying magnitude
and the polarity of the bias voltage can be controlled, via PID action,
so as to drive the electrical resistance of the memristor 502 between
values 610 and 606 is less time than during time period 12. It is further
noted that the PID controller 522 continuously senses the balance
condition of the Wheatstone Bridge 512--and thus, the instantaneous
resistance of the memristor 502--by way of the error signal at node 520,

[0057] The controller 500 is configured to monitor a balanced or out-of
balance condition of the Wheatstone Bridge 512 in accordance with the
presently desired resistance value for the memristor 502. That is,
particular voltages sensed across the Wheatstone Bridge 512 are
correlated to particular memristor 502 resistance values. Thus, the PID
controller 522 is configured to control the source 504 so as to adjust
the memristor 502 from a first resistance value (e.g., 606, etc.) to a
second resistance value (e.g., 610, etc.) in a predetermined time period
and with minimal or no overshoot.

[0058] Resistances that lie within the range defined by the rail-to-rail
values 602 and 604 can be programmed into the memristor 502 so as to
maximize the useful life of the memristor 502. The time periods used
during adjustment (e.g., T2 and T4, etc.) can also be controlled by the
PID controller 522 in the interest of memristor 502 endurance.

[0059] In general, the foregoing description is intended to be
illustrative and not restrictive. Many embodiments and applications other
than the examples provided would be apparent to those of skill in the art
upon reading the above description. The scope of the invention should be
determined, not with reference to the above description, but should
instead be determined with reference to the appended dams, along with the
full scope of equivalents to which such cams are entitled. It is
anticipated and intended that future developments will occur in the arts
discussed herein, and that the disclosed systems and methods will be
incorporated into such future embodiments. In sum, it should be
understood that the invention is capable of modification and variation
and is limited only by the following claims.